Step-by-Step: How to Solve Linear Equations

Welcome to the world of linear equations! Today we'll explore their fundamental properties.A linear equation is an equation where variables are only raised to the first power - no squares, cubes, or other exponents.Let's look at some examples of linear and non-linear equations to understand the difference.Now, let's learn the golden rule of solving equations: whatever operation you perform on one side, you must do the same to the other side.Think of an equation like a balance scale - it must always stay equal on both sides.Our ultimate goal is to isolate the variable - to get x by itself on one side of the equation.Let's look at this step-by-step process. We start with our equation: two x plus five equals thirteen.To isolate x, we first subtract five from both sides of the equation.The fives cancel out on the left side, leaving us with two x equals eight.Now that we understand the basic rules, we're ready to solve more complex equations.Let's solve equations using addition and subtraction.Remember, an equation is like a balance scale - what we do to one side, we must do to the other.To solve for x, we need to isolate it by removing the positive six from both sides.When we subtract six from both sides, the equation stays balanced.This gives us our solution: x equals four.Let's try an equation with subtraction: x minus three equals seven.To remove a negative term, we add its opposite. Here, we add positive three to both sides.This gives us x equals ten.Now let's solve an equation with negative numbers: x plus negative two equals five.When we have negative two, adding positive two will get us back to zero.This gives us x equals seven.For our final example, let's solve x minus negative four equals three.When we subtract a negative number, it's the same as adding its positive. So minus negative four becomes plus four.This gives us our final answer: x equals negative one.Let's solve an equation with multiplication. Here we have three x equals fifteen.To isolate x, we need to divide both sides by three.This gives us x equals five.Now let's solve an equation with division. Here we have x divided by four equals five.To isolate x, we multiply both sides by four. This cancels out the division on the left side.This gives us x equals twenty.Let's solve a more complex equation that combines multiple operations: two x plus four equals twelve.First, we subtract four from both sides to isolate the term with x.Now we have two x equals eight. To isolate x, we divide both sides by two.This gives us our final answer: x equals four.